Question

Find an equation for the nth term of the arithmetic sequence.a16 = 21, a17 = -1

Answer 1

the general equation for the nt term of an arithmetic progression is
\[T _{n} = a + ( n -1 ) d\]
where
" Tn" is the n th term
" a" is the first term
"d" is the common difference...

so...
from ur data
a 16 = 21
a 17 = -1

apply this data to the above formula..
for a16
Tn = a + (n-1)d
a16 = a + (16 -1)d
21 = a + 15d ------(1)

for a17
Tn = a + (n-1)d
a17 = a + (17 -1)d
-1 = a + 16d ----(2)

now
(1) - (2)
21- (-1) = a + 15d - ( a + 16d)
22 = a + 15d -a -16d
22 = -d
d = -22

now substitute d =(-22) in (1)
21 = a + [15x(-22)]
21= a -330
a = 330 +21
a = 351

so...
now u know the values
a =351
d = -22

so.. the nth term is...
\[T _{n} = a + ( n -1 ) d\]
\[T _{n} = 351 - ( n -1 ) 22\]

hope this will help ya!!!

Answer 2

Is this the same as your answer an = 351 - 22(n - 1)

Answer 3

yep!!

Answer 4

Thank You !